---
title: "Single-storey external wall: stress, brick, mortar"
subject: "Concrete Technology and Masonry Structure"
chapter: 8
key: "semester_5/concrete_technology_and_masonry_structure:wall-single-storey-100kn-12mm"
source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/wall-single-storey-100kn-12mm
site: BCT Engineering
---

# Single-storey external wall: stress, brick, mortar

Concrete Technology and Masonry Structure · Chapter 8: Design of masonry walls for gravity loads

- Asked in: 2078 Kartik, 12 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/wall-single-storey-100kn-12mm
- Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-8

## Question

An external wall of a single storeyed building is 23 cm thick and carries 100 kN/m load at the top of the wall with an eccentricity of 12 mm. The plinth level is 1.5 m above the top of foundation footing and floor to ceiling height is 3.0 m. The RCC slab bears on the wall and is 12 cm thick. Determine the maximum stress in the wall and calculate the strength of brick and grade of mortar required for the wall. Assume necessary data if any required.

## Short answer

Maximum stress 0.66 N/mm². Required basic compressive stress 0.57 N/mm². Use bricks of crushing strength not less than 7.5 N/mm² with M2 mortar (cement:sand 1:6), giving permissible stress 0.59 N/mm².

## Answer

#### Data and assumptions

- Wall 230 mm thick, modular bricks ($k_p=1$); load at top 100 kN/m with eccentricity 12 mm, so $e/t=12/230=0.0522$ ($>1/24$).
- Plinth 1.5 m above top of footing, ceiling height 3.0 m, 12 cm RCC slab bearing on the wall. Walls longer than $h_{ef}$ (no cross walls given), so height governs.
- Brick masonry 19 kN/m$^3$. Design by IS 1905:1987; NBC 109 follows the same method. Critical section: base of wall at the top of the footing.

#### Step 1: Effective height and slenderness ratio

Height from top of footing to the centre of slab $H = 1.5+3.0+0.12/2 = 4.56$ m (IS 1905 Table 4 Note 1). The footing and the RCC slab give full restraint, so $h_{ef}=0.75H$:

$$
\begin{aligned} h_{ef} &= 0.75\times4.56 = 3.420\ \text{m}\\ SR &= \frac{3.420}{0.23} = 14.87\ (<27) \end{aligned}
$$

#### Step 2: Load and maximum stress at the base

$$
\begin{aligned} \text{Self weight} &= 0.23\times4.5\times19 = 19.67\ \text{kN/m}\\ P &= 100+19.67 = 119.67\ \text{kN/m}\\ M &= 100\times0.012 = 1.20\ \text{kNm/m}\\ \sigma_{max} &= \frac{P}{A}+\frac{6M}{t^2} = \frac{119.67\times10^3}{230\times10^3}+\frac{6\times1.20\times10^6}{1000\times230^2} = 0.520+0.136 = 0.656\ \text{N/mm}^2 \end{aligned}
$$

(At the top of the wall, under the load alone, $\sigma_{max}=\frac{100\times10^3}{230\times10^3}(1+\frac{6\times12}{230}) = 0.571$ N/mm$^2$.) The maximum stress in the wall is **0.656 N/mm$^2$** at the base (compression; no tension since $e<t/6$).

#### Step 3: Factors and required basic stress

- $k_s$ (Table 9, $SR=14.87$, $e/t=0.052$, interpolated) $= 0.732$
- $k_a=1.0$ (area 0.23 m$^2$/m), $k_p=1.0$
- $e/t>1/24$: 25 percent increase allowed (cl. 5.4.1.4 a)

$$
f_b \ge \frac{\sigma}{k_sk_ak_p\times1.25} = \frac{0.520}{0.732\times1.25} = 0.569\ \text{N/mm}^2
$$

#### Step 4: Brick and mortar (IS 1905 Table 8)

| Mortar (IS 1905 Table 1) | Min. unit strength (N/mm²) | Table 8 $f_b$ (N/mm²) |
|---|---|---|
| M2 (cement:sand 1:6) | 7.5 | 0.59 |
| M1 (cement:sand 1:5) | 7.5 | 0.74 |
| H2 (cement:sand 1:4) | 7.5 | 0.74 |
| H1 (cement:sand 1:3) | 7.5 | 0.75 |

**Answer: maximum stress = 0.656 N/mm$^2$. Required $f_b = 0.569$ N/mm$^2$, so use bricks of crushing strength not less than 7.5 N/mm$^2$ with M2 mortar (1:6, $f_b=0.59$ N/mm$^2$).** A richer mortar (M1, H2, H1) also needs 7.5 N/mm$^2$ units, so there is no gain from a stronger mortar here.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. H for the effective height is measured from:
   A. Plinth to ceiling, 3.0 m
   B. Top of footing to centre of slab: 1.5 + 3.0 + 0.06 = 4.56 m
   C. Top of footing to ceiling, 4.5 m
   D. Ceiling height only plus 0.12
   Answer: B. IS 1905 Table 4 Note 1: height to centre of slab from footing top, giving 4.56 m, h_ef = 0.75H = 3.42 m, SR = 14.87. (Key point: Height H)

2. Maximum stress at the base is P/A + 6M/t^2. What is e/t and the result?
   A. e/t = 0.052 and sigma_max = 0.656 N/mm^2
   B. e/t = 0.12 and 1.2 N/mm^2
   C. e/t = 0.052 and 0.520 N/mm^2
   D. e/t = 0.5 and 0.1 N/mm^2
   Answer: A. e/t = 12/230 = 0.052 < 1/6 so no tension; 0.520 + 0.136 = 0.656 N/mm^2. (Key point: Maximum stress)

3. Is the 25 percent increase allowed here?
   A. No, e/t is below 1/24
   B. Yes, e/t = 0.052 exceeds 1/24 (0.042)
   C. No, because the wall is external
   D. Only for lime mortar
   Answer: B. 1/24 = 0.0417 and e/t = 0.052 is greater, so the increase applies. (Key point: Why 25 percent increase)

4. Required f_b = 0.520/(0.732 x 1.25) = 0.569. Which unit works with M2?
   A. 3.5 N/mm^2
   B. 5 N/mm^2 with 0.44
   C. 7.5 N/mm^2 with 0.59
   D. 10 N/mm^2 only
   Answer: C. M2 with 7.5 N/mm^2 gives 0.59 >= 0.569; richer mortar gives no gain at that unit strength. (Key point: Selection)

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